THIRD APPROXIMATION

merely preparatory to the third, which alone correspondsto the actual world of facts. Yet the other two approxi-mations are of even greater importance than the thirdfrom the point of view of theoretical analysis. They tellus what would happen under their respective hypotheses.Both these hypotheses are simpler than reality; hencethey lend themselves better to formal analysis andmathematical expression.

Moreover, to know what would happen under thesehypothetical conditions enables us better to understandwhat does happen under actual conditions, just as theknowledge that a projectile would follow a parabola ifit were in a vacuum enables the student of practicalgunnery better to understand the actual behavior of hisbullets or shells. In fact, no scientific law is a perfectstatement of what does happen, but only what wouldhappen if certain conditions existed which never do actu-ally exist . 10 Science consists of the formulation of con-ditional truths, not of historical facts, though by suc-cessive approximations, the conditions assumed may bemade nearly to coincide with reality . 11

The second approximation gives a clear cut theoryapplicable to the clear cut hypotheses on which it isbased. The third approximation cannot avoid somedegree of vagueness.

10 See the writer’s Economics as a Science, Proceedings of the AmericanAssociation for Advancement of Science, Yol. LVI, 1907.

“See Appendix to Chapter IX, No. 1.

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